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Boundary homogenization for a triharmonic intermediate problem
Author(s) -
Arrieta José M.,
Ferraresso Francesco,
Lamberti Pier Domenico
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4025
Subject(s) - homogenization (climate) , mathematics , bounded function , mathematical analysis , perturbation (astronomy) , homogeneous , boundary value problem , euclidean geometry , geometry , combinatorics , physics , biodiversity , ecology , biology , quantum mechanics
We consider the triharmonic operator subject to homogeneous boundary conditions of intermediate type on a bounded domain of the N‐dimensional Euclidean space. We study its spectral behaviour when the boundary of the domain undergoes a perturbation of oscillatory type. We identify the appropriate limit problems that depend on whether the strength of the oscillation is above or below a critical threshold. We analyse in detail the critical case that provides a typical homogenization problem leading to a strange boundary term in the limit problem. Copyright © 2016 John Wiley & Sons, Ltd.